What I Learned from A Mind For Numbers by Barbara Oakley

Focus vs. Diffuse Thinking

Learning requires switching between two modes:

• Focused mode: when you’re locked in, working through details.
• Diffuse mode: when your brain wanders, making connections in the background.

Taking a break is part of working. Just like muscles need recovery between sets and workouts, the brain needs downtime for deep learning.

A great way to utilize diffuse mode is while being active, walking outside, running, or even doing housework.

Learning Slow Means Learning Deep

We all know that learning fast isn’t the same as learning well. Rushing leads to shallow understanding. Instead, spreading practice into short, daily sessions makes knowledge automatic. It’s just like working out. To build muscles, you don’t rush; you increase the weight gradually, with patience and consistency.

Even recalling information in different places helps lock it in. This could be at home, outside, or in class, for example.

It’s About the Process, Not the Product

Cramming the night before an exam is like going for your first run the day before a marathon. It doesn’t work. What matters is the process: daily practice, testing yourself, reviewing, and redoing.

When doing homework, the main focus shouldn’t be on finishing, but on the work itself. Treat each assignment as training for the test. Every session is a workout that slowly and methodically builds the skill.

Active Learning Beats Passive Learning

Some study methods feel productive but aren’t. Highlighting, for example, gives the illusion that what’s colored is already learned, or that anything not highlighted is unimportant when in fact it is.

Here’s what actually works:

• Active recall: testing yourself without looking at the answer.
• The Feynman technique: explaining concepts simply, as if teaching.
• The Pomodoro method: short, focused sprints with breaks in between.

Managing Willpower and Stress

Willpower is like a muscle: you can use it, but it gets tired. That’s why habits matter. They save willpower for when you really need it. (For more on habits, check out my takeaways from Atomic Habits by James Clear.)

Stress can also be valuable. Not panic-level stress, but just enough challenge to stay engaged. During exam prep, time yourself solving questions, or practice in a classroom setting. On test day, start by skimming all the exercises. Begin with the hardest, and when you get stuck, switch to an easier one. That puts the hard problem into diffuse mode while you make progress.

Mindsets That Matter

A eureka moment, when you finally grasp a solution, isn’t the end. What matters is understanding how the solution came about and reviewing it the same day.

If you’re doubting your intellect, skills, or accomplishments, you’re not alone; even experts feel imposter syndrome. And if you’re frustrated by low grades, remember: they may just mean you’re approaching problems differently. That difference could make you a more creative thinker. Nobody is “not good” at learning; they may just not have been exposed to all the lenses yet.

Experiment, Compete, Improve

Learning is a cycle of self-experimentation: try methods, determine what sticks, adjust. But it’s also important to distinguish between training (homework, practice) and competition (tests, real applications). Both are essential. Athletes don’t always win every competition, but they learn from each attempt and improve.

And mastery doesn’t mean you have to stick with something forever. It means building the skill so you can move on. It’s okay to “get good and then quit.”

Shared Wisdom

Learning is not just personal, it’s collective. Sharing ideas, questioning weak arguments, and working back and forth sharpens understanding. A good study environment is one where study wins over chatter.

If you’re in the same room as a friend, try doing the same homework separately and only asking for help when stuck. If you’re in different places, work on the same questions individually, then compare answers. If your answers differ, redo the exercise and compare again.

The Einstellung effect occurs when a pre-existing solution blinds you and blocks problem-solving. That’s why collaboration is key to opening your horizons. Techniques like diffuse-mode thinking also help your brain connect dots you wouldn’t have made otherwise.

My Final Thoughts

I found the book’s strategies really helpful. One technique they used that I especially liked was ending chapters with active recall questions.

Like with Atomic Habits, I felt at first that I “already knew” much of what the author would say. I was wrong. The insights run much deeper once you apply them. That said, the book isn’t the easiest read. Not because it’s complex, but because the ideas are scattered. For this article, I actually had to reorder and regroup my notes to make sense of it all.

Still, the effort was worthwhile, and I recommend this book to anyone wishing to improve their learning.